Enumeration of curves with two singular points
Algebraic Geometry
2015-12-29 v1 Algebraic Topology
Abstract
In this paper we obtain an explicit formula for the number of curves in two dimensional complex projective space, of degree d, passing through d(d+3)/2-(k+1) generic points and having one node and one codimension k singularity, where k is at most 6. Our main tool is a classical fact from differential topology: the number of zeros of a generic smooth section of a vector bundle V over M, counted with a sign, is the Euler class of V evaluated on the fundamental class of M.
Cite
@article{arxiv.1409.6702,
title = {Enumeration of curves with two singular points},
author = {Somnath Basu and Ritwik Mukherjee},
journal= {arXiv preprint arXiv:1409.6702},
year = {2015}
}
Comments
56 pages, 1 figure; comments are welcome. arXiv admin note: text overlap with arXiv:1308.2902